Wavy Fin Structure and Flat Tube Heat Exchanger Having the Same

ABSTRACT

Disclosed are a wavy fin structure, in which a cross-cut having a designated length is formed at a designated position of a wavy fin, and a flat tube heat exchanger having the same. The cross-cut is formed around at least one valley or peak of the fin. One cross-cut is formed at a valley or a peak at the central portion of the fin or a plurality of cross-cuts is formed at designated periods in the length direction of the fin. Further, the cross-cut is formed at a position at the rear of the peak and the length of the cross-cuts is 
     
       
         
           
             
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     The wavy fin structure generates flow disturbance due to a wavy-type dynamic flow, thus improving heat transfer performance.

CROSS-REFERENCE TO RELATED APPLICATION

This U.S. patent application claims the benefit of priority under 35U.S.C. §119 of Korean Patent Application No. 10/2014/0175913, filed Dec.9, 2014, the entire content of which is hereby incorporated herein byreference for all purposes.

TECHNOLOGICAL FIELD

The present disclosure relates to a wavy fin structure and a flat tubeheat exchanger having the same, and more particularly to a wavy finstructure which may further improve heat exchange performance of a fluidand a flat tube heat exchanger having the same.

BACKGROUND

In general, a heat exchanger is an apparatus which executes heatexchange between two different fluids separated from each other by asolid wall and is widely used in industrial fields, such as heating, airconditioning, power generation, waste heat recovery, chemical processesand the like. There are various types of heat exchangers and,thereamong, a fin-type heat exchanger having an expanded heat transfersurface, which has a simple structure and is easily manufactured, iswidely used now. In order to improve heat transfer performance of thefin-type heat exchanger, research on change of the shape of fins at anoperating fluid side has been carried out and, as kinds of compact heatexchangers having a small size and a light weight which have beendeveloped, there are a louvered fin-type heat exchanger, an offset stripfin-type heat exchanger, a wavy fin-type heat exchanger and the like.

There among, a wavy fin is easily manufactured, as compared to otherhigh-performance fins, and is easily applied to a fin-flat tube heatexchanger. The wavy fin is formed by modifying a general plain fin intoa wavy type in a flow direction and thus increases a heat transfer area,and dynamically forms a flow and thus increases heat transferperformance. Further, a wavy fin-type heat exchanger is advantageous inthat it has high heat transfer performance and is less influenced bydust, thus being usable in a wide variety of environments. FIG. 1 is aview illustrating surfaces of a wavy fin structure which is applied to aflat tube and FIGS. 2(a) and 2(b) are photographs of a general wavy finstructure.

Research on a wavy fin-type heat exchanger was executed by manyinvestigators through experimentation and numerical analysis. In thecase of a wavy fin, it is known that a flow of the wavy fin isdynamically formed in the wavy shape of the fin and divided into alaminar flow region, an abnormal region in which a longitudinal vorticeis formed, and a turbulent flow region, and important shape parametersinfluencing wavy fin performance include a wavelength, a warpage angle,a fin pitch and the like. Further, Korean Patent Laid-open PublicationNo. 10-2013-0059784 (Publication Date: Jun. 7, 2013) discloses a wavyfin structure which partially structurally changes fins so as to promoteturbulence of a fluid and to improve heat exchange efficiency of thefluid.

Cross-Cutting means a technique in which a fin is cut into a designatedlength in a direction vertical to the flow direction of a fluid so as toimprove heat transfer performance. In ‘Fluid flow and heat transfercharacteristics of cross-cut heat sinks (Tae Young Kim and Sung Jin Kim,International Journal of Heat and Mass Transfer 52, pp. 5358-5370,2009)’, heat transfer performance improvement effects, through anexperiment in which cross-cuts are applied to a plain fin, wereconfirmed. In general, it is known that, if cross-cuts are applied to afin, a thermal boundary layer collapses, heat transfer in the lengthdirection is blocked and, thus, heat transfer performance is improved.

SUMMARY OF THE DISCLOSURE

Therefore, the present disclosure has been made in view of the aboveproblems, and it is an object of the presently described embodiments toprovide a wavy fin structure, which may further improve heat exchangeperformance of a fluid by applying cross-cuts to wavy fins, and a flattube heat exchanger having the same.

In accordance with an aspect of the presently described embodiments, theabove and other objects can be accomplished by the provision of a wavyfin structure in which fins are periodically arranged in a plurality ofrows and each fin is periodically waved to form repeated valleys andpeaks in the length direction of the fin, wherein a cross-cut having adesignated length is formed around at least one valley or peak of thefin.

Here, one cross-cut may be formed at a valley or a peak of the centralportion of the fin in the length direction of the fin or a plurality ofcross-cuts may be formed at designated periods in the length directionof the fin.

The cross-cut may be formed at a position at the rear of the peak.

The length of the cross-cut may be

${\frac{1}{5}C\mspace{14mu} {to}\mspace{14mu} \frac{4}{5}C},$

C may be

$\frac{b}{2\mspace{14mu} {\sin (\alpha)}},$

α may be a warpage angle of the fin, and b may be a fin pitch.

In accordance with another aspect of the presently describedembodiments, there is provided a flat tube heat exchanger having thewavy fin structure.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and other advantages of thepresently described embodiments will be more clearly understood from thefollowing detailed description taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is a conceptual view illustrating a general flat tube and wavyfins applied thereto;

FIGS. 2(a) and 2(b) are photographs illustrating perspective and planviews of a general wavy fin structure;

FIGS. 3 and 4 are views illustrating the geometric structure of a wavyfin with cross-cuts applied to embodiment 1 of the present disclosure;

FIG. 5 is a view illustrating distributions of temperature contour linesof a wavy fin without cross-cuts (da=0 m) and wavy fins with cross-cutsin accordance with embodiment 1 (da=0.001 m, 0.003 m);

FIGS. 6(a) and 6(b) are views illustrating the geometric structure of awavy fin applied to tests of embodiment 2 and embodiment 3 and FIG. 6(c)is a view illustrating a non-uniform grid state of the wavy fin;

FIG. 7 is a view illustrating graphs representing validation results off (upper) −Nu_(lm) (low) of the wavy fin of FIG. 6 under the conditionof 100≦Re≦400;

FIG. 8 is a view illustrating the geometric structure of the wavy fin inaccordance with embodiment 2 in which cross-cuts are applied topositions in front of and at the rear of peaks;

FIG. 9 is a view illustrating graphs representing results ofNu/Nu_(nocut) (upper) and f/f_(nocut) (lower) when cross-cuts areapplied to positions in front of and at the rear of peaks of the wavyfin in accordance with embodiment 2;

FIGS. 10(a) to 10(c) are views illustrating distributions ofnon-dimensionalized velocity (upper)—temperature contour lines of a wavyfin without cross-cuts ((a) Nocut) and wavy fins with cross-cuts inaccordance with embodiment 2 ((b) Front cut) ((c) Back cut) under an Reof 400;

FIG. 11 is a view illustrating the geometric structure of the wavy finin accordance with embodiment 3 to which cross-cuts having variouslengths are applied to a region at the back of a peak of the wavy fin;

FIG. 12 is a view illustrating graphs representing results ofNu/Nu_(nocut) (upper) and f/f_(nocut) (lower) when cross-cuts havingvarious lengths are applied to positions in front of peaks of the wavyfin in accordance with embodiment 3;

FIG. 13 is a view illustrating distributions of non-dimensionalizedvelocity (upper)—temperature contour lines of the wavy fin in accordancewith embodiment 3 when cross-cuts having various lengths are applied topositions in front of peaks of the wavy fin;

FIG. 14 is a graph illustrating results of Nu distributions when nocross-cuts are present and in case 3 and case 4 of embodiment 3 under anRe of 400;

FIG. 15 is a view illustrating a velocity streamline distribution(upper) and a pressure contour line distribution (lower) under an Re of400 in part 6 of case 3 of embodiment 3;

FIG. 16 is a graph illustrating a result of j/f values when nocross-cuts are present and in case 3 of embodiment 3 under the conditionof 100≦Re≦400; and

FIG. 17 is a view illustrating graphs representing results of levels ofusefulness (c) and Nu values when no cross-cuts are present (0) and inthe respective cases of embodiment 3 under an Re of 400.

DETAILED DESCRIPTION

Now, a wavy fin structure and a flat tube heat exchanger having the samein accordance with preferred embodiments in accordance with the presentdisclosure will be described in detail with reference to the annexeddrawings.

As described above, a wavy fin-type heat exchanger has a flat tubethrough which a fluid may pass and a wavy fin structure to induceturbulence of the fluid to improve heat exchange efficiency is installedwithin the flat tube. The flat tube heat exchanger is well known tothose skilled in the art and a detailed description thereof will thus beomitted.

In the wavy fin structure, as exemplarily shown in FIG. 2, fins areperiodically arranged in a plurality of rows in the width direction ofthe wavy fin structure and upper and lower ends of the respective finsare bonded to a flat tube. The wavy fin structure is configured suchthat the fins are periodically waved to form a plurality of peaks andvalleys in the length direction thereof, i.e., the flow direction of afluid and, thus, a plurality of fluid passages are formed within thewavy fin structure so as to be divided from each other. Therefore, thefluid passing through the fluid passages of the wavy fins flows throughthe wavy structure, thus inducing turbulence and stirring.

In accordance with the presently described embodiments, cross-cuts whichare cut vertically to the length direction of the fins, i.e., the flowdirection of the fluid, are formed on the wavy fin structure. Thecross-cut may be formed around at least one valley or peak of the wavyfin. One cross-cut may be formed at the valley or peak of the centralportion of the wavy fin or a plurality of cross-cuts may be formed atvalleys or peaks of the fin periodically.

Cross-Cuts are applied to various positions of wavy fins in accordancewith various embodiments, which will be described later, or heattransfer performances acquired by applying cross-cuts having variouslengths are confirmed through experimentation. If cross-cuts are appliedto wavy fins, flow disturbance may be generated due to a dynamic flow ofa wave type and heat transfer performance may be further increased.

Hereinafter, various embodiments will be described.

Embodiment 1—Formation of Cross-Cuts at Valleys or Peals of Wavy Fins

In this embodiment, a cross-cut having a designated size is formedaround a valley or a peak around the central portion of a wavy fin andhas a basic shape, as exemplarily shown in FIGS. 3 and 4. Here, it maybe interpreted that a valley or a peak means the lowest point (lowestposition) and the highest point (highest position) and ‘a region arounda valley or a peak’ means a peripheral region including the valley orthe peak. Further, in the embodiment, the wall of the wavy fin has aplanar surface (a linear cross-section).

As exemplarily shown in FIGS. 3 and 4, in this embodiment, performanceexperimentation is executed using a 5 wave wavy channel, a cross-cut isformed at the central portion (the third wave), the length of one cycleof a fin is 10.8 mm, and a fin pitch is 2.5 mm. Further, the thicknessof the fin is 0.2 mm, the height of the fin is 8 mm, and the fin isformed of aluminum.

An analysis region for numerical analysis is configured so as tocompletely represent the wavy fin and the channel of air. The flat tubeto which the wavy fins are applied has a completely symmetrical shape inthe height direction and thus, in order to reduce the analysis region,only the half of the flat tube in the height direction is modeled, and asymmetry boundary condition is input to the upper surface of theanalysis region. Further, since the wavy fins are periodically arranged,modeling is executed over only one row not the entire model and aperiodic boundary condition is given. Air flows along the surfaces ofthe fins from right to left. The velocity profile of air is not uniformat the inlet of the channel including the surfaces of the fins and theflat wall of the fins due to the thickness of the fins. For this reason,the analysis region has clearances having designated distances at theinlet and the outlet (inlet: 10.8 mm corresponding to the length of onecycle of the wavy fin, outlet: 21.6 mm corresponding to the length oftwo cycles of the wavy fin).

FIG. 5 illustrates temperature distributions if a cross-cut is formed atthe centers of wavy fins. In FIG. 5, the first graph illustrates atemperature distribution if no cross-cut is formed at a wavy fin (nocut, d_(a)=0 m) and the second and third graphs illustrate temperaturedistributions if cross-cuts having different lengths are formed at wavyfins (d_(a)=0.001 m, d_(a)=0.003 m). As exemplarily shown in FIG. 5, itmay be confirmed that temperatures at the cross-cuts are lowered. It maybe understood that, if a cross-cut is formed, a flow boundary layer isdestroyed and regenerated and such a process disturbs a stagnant thermalflow.

Embodiment 2—Research on Optimal Position of Cross-Cut

In accordance with embodiment 1, it may be understood that, if across-cut is formed around the valley or the peak of the center of awavy fin, heat transfer performance is improved.

Further, embodiment 2 and embodiment 3 represent test examples to findthe optimal position and length of a cross-cut.

In embodiment 2 and embodiment 3, all computational fluid dynamics (CFD)analysis is two-dimensionally carried out. With reference to FIGS. 6(a)to 6(c), a type of a 5 wave wavy channel (b/Lc=0.15) having a fin pitch(b) of 6.9 mm, a 1 cycle of wavy fins (Lc) of 45.7 mm, and a warpageangle of 20°, and used in a flow visualization test of Ali andRamadhyani (W. M. Kays., A. L. London, Compact Heat Exchangers, 3rdedition, McCraw-Hill, New York, 1984.), which is non-dimensionalizedinto a hydraulic diameter, is used in analysis. The hydraulic diameterand an Re value are calculated by Equation 1 below. All equations referto those given in Viscous Fluid Flow (Third edition, McGraw-Hill, NewYork, 2006) of Frank M. White.

$\begin{matrix}{{{Dh} = {{\lim\limits_{w\rightarrow\infty}\frac{2{wb}}{\left( {w + b} \right)}} = {2b}}}{{Re} = \frac{U_{in}D_{h}}{v}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

As exemplarily shown in FIG. 6(b), information regarding the analyzedshape has b of 0.5 D_(h) and L_(c) of 3.312 D_(h) as anon-dimensionalized result of a length dimension. Further, in the samemanner as the shape used in the Ali and Ramadhyani test, clearanceshaving designated distances are given to the inlet and the outlet(inlet: 1.036 5 D_(h), outlet: 1.267 D_(h)).

A designated temperature condition is given to the wall surface as theboundary condition, a designated velocity condition is used as an inletvelocity, and a pressure condition is used as an outlet condition. Anoperating flow region is fixed to a region satisfying 100≦Re≦400, whichis reported as a normal laminar flow in the Ali and Ramadhyani paper.

FIG. 6(c) illustrates the state of a grid which is used. A structuredgrid is used in a direction parallel with a fin wall and an unstructuredgrid which is more densely formed around the wall is used in a directionvertical to the fin wall. A grid dependency test is carried out using aNu value and an f value of a flow having an Re of 400 in a wavy shape towhich no cuts are applied. The Nu value and the f value are calculatedby Equation 2 below.

$\begin{matrix}{{f = \frac{\Delta \; p^{*}}{2L*}}{{Nu} = {\left| \frac{\partial\theta}{\partial n^{*}} \right| = {\frac{Q_{w}}{A_{s}\left( {T_{w} - T_{in}} \right)}\frac{D_{h}}{k}}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In Equation 2 above, L* is a non-dimensionalized value of the totallength of a wavy fin. N* means a direction vertical to the fin wall.A_(s) means the total heat transfer area.

Table 1 below represents results of an f-Nu grid dependency test toanalyze an Re 400 wavy fin.

TABLE 1 Mesh Friction factor Nu Number (% deviation) (% deviation) 76000.106173101 10.86369 13250 0.103713962 (2.32) 10.20564 (6.05) 204000.102659318 (1.02) 9.829024 (3.70) 29050 0.102136701 (0.51) 9.609202(2.24) 39200 0.101836291 (0.29) 9.476781 (1.38) 50850 0.101622992 (0.21)9.395578 (0.86) 64000 0.101465841 (0.15) 9.344464 (0.54)

A result of the grid dependency test, a grid of a mesh number of 29050having a fraction factor and a Nu value, deviations of which are lessthan 1.5%, is used to execute analysis.

Validation of such analysis is carried out by comparing f-Nu analysisresults to test result values proposed by the Ali and Ramadhyani test. Amethod for calculating an f value is the same as in the previous griddependency test. However, as a Nu value, a Nu_(lm) value used in the Aliand Ramadhyani research is calculated and compared using Equation 3below. A difference between T_(w) and T_(in) is calculated as 10° C.

$\begin{matrix}{{{Nu}_{lm} = {\frac{Q_{w}}{{A_{s}\left( {\Delta \; T} \right)}_{Lm}}\frac{D_{h}}{k}}}{{\Delta \; T_{lm}} = \frac{\left( {T_{w} - T_{in}} \right) - \left( {T_{w} - T_{out}} \right)}{\ln \left\lbrack {\left( {T_{w} - T_{in}} \right) - \left( {T_{w} - T_{out}} \right)} \right\rbrack}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

FIG. 7 illustrates validation results and it is judged that analysisfollows tendency of test results well. It may be understood that, as anRe value increases, both heat transfer performance and pressure lossincrease. As results of the All and Ramadhyani test, an increasegradient of the Nu value is changed within the range of 100≦Re≦400, andit is reported that it is caused by effects of longitudinal (Goertler)vortices. In such research, analysis is carried out only within therange of 100≦Re≦400 and, thus, effects of longitudinal (Goertler)vortices are not confirmed.

In order to find the optimal position of a cross-cut, a cut having asize of 0.145 D_(h) is applied to a position in front of a peak and aposition at the rear of a peak of the center of an analysis model (thethird wave), as exemplarily shown in FIG. 8, and thus heat transferperformance and pressure loss are compared. In terms of the inner flowof a wavy fin, a recirculation section is generated around a peak andheat transfer performance is relatively low. Therefore, a cross-cut isapplied to a region around the peak.

As exemplarily shown in FIG. 8, cross-cuts are implemented by cutting apart of a fin wall by 0.145 D_(h) under a periodic condition. Heattransfer performance and pressure loss are estimated using f and Nuwhich are used in the grid dependency test.

FIG. 9 illustrates results of the above test. If a cross-cut is appliedto a position in front of a peak (front position), a Nu value increasesby up to 5.71% at an Re of 400, as compared to the shape to which nocross-cut is applied. In this case, an f value increases by up to 4.56%at an Re of 400. If a cross-cut is applied to a position at the rear ofa peak (back position), a Nu value increases by up to 14.14% at an Re of400 and an f value increases by up to 5.10% at an Re of 400. In general,as an Re value increases, heat transfer performance and pressure lossincrease. It is known that, if a cross-cut is applied, collapse of athermal boundary layer of a flow at the applied part and blocking ofheat transfer in the length direction due to a temperature differencebetween front and rear parts of a fin are simultaneously achieved and,thus, heat transfer performance is improved. However, in the case ofthis test, since two-dimensional analysis is carried out, blocking ofheat transfer in the length direction may not be confirmed. Therefore,actual heat transfer improvement effects may be further increased, ascompared to heat transfer improvement represented in this test.

Now, performances according to application positions of cross-cuts willbe compared. It may be confirmed that heat transfer performance if across-cut is applied to a back position is about 3 times heat transferperformance if a cross-cut is applied to a front position. On the otherhand, it may be confirmed that pressure loss is increased only by 1%and, thus, application of a cross-cut to a back position is moreeffective. The reason for this is that, if a cross-cut is applied to afront position, the cut is horizontal with the flow direction and flowdisturbance effects are few, and if a cross-cut is applied to a backposition, flow collides with the fin at the rear of the cut and obliqueimpinging-type flow disturbance is actively generated. This may beeffectively confirmed through FIGS. 10(a) to 10(c). FIG. 10(a)represents results if no cross-cut is formed (no cut), FIG. 10(b)represents results if a cross-cut is formed at a position in front of apeak (front cut), and FIG. 10(c) represents if a cross-cut is formed ata position at the rear of a peak (back cut). Consequently, it may beconfirmed that application of a cross-cut to a position at the rear of apeak is more effective.

As described above, it is confirmed that heat transfer performance if across-cut is applied to a position at the rear of a wave peak is about 3times heat transfer performance if a cross-cut is applied to a positionin front of a wave peak. The reason for this is that, if a cross-cut isapplied to a position in the front of a wave peak, the cross-cut ishorizontal with the flow direction and flow disturbance effects are few,and if a cross-cut is applied to a position at the rear of a wave peak,the cross-cut is not horizontal with the flow direction and flowdisturbance effects are great. Additionally, due to active flowdisturbance, pressure loss if a cross-cut is applied to a position atthe rear of a wave peak is relatively great but a difference betweenpressure losses at the front position and the back position is notgreat.

Embodiment 3—Research on Optimal Length of Cross-Cut

In the previous embodiment, it is confirmed that heat transfer effectsare great if a cross-cut is formed at a position at the rear of a peak.In this embodiment, research to find the optimal length of a cross-cutwhen the cross-cut is located at a position at the rear of a peak iscarried out.

This research is carried out using C=b/(2 sin(α)) which is influenced bya fin pitch (b) and a warpage angle (α), as exemplarily shown in FIG.11. Total 5 cut lengths of 0.145 P_(h), 0.292 D_(h)(2/5 C), 0.365D_(h)(1/2 C), 0.585 D_(h)(4/5 C), and 0.731 D_(h)(C) are implemented andcompared and FIGS. 12 and 13 illustrate results of comparison betweenthese lengths.

First, as compared to a shape to which no cross-cut is applied, case 2(2/5 C) exhibits heat transfer performance which is increased by up to22.9% and causes maximum performance improvement. It is confirmed that,in case 2, maximum flow disturbance is generated. When a flow occursbetween fins, a thermal boundary layer is formed from the fin wall andthe temperature of the central portion of the flow is lower than thetemperature of the wall. Here, if a cross-cut having the length of case2 is applied, impinging-type flow disturbance is formed at the centralportion of the flow having the relatively low temperature and heattransfer performance is rapidly increased.

On the contrary, case 4 (4/5 C) does not effectively cause disturbanceof the central portion of a flow due to an excessively long length ofthe cross-cut and forms the flow, the entirety of which passes throughthe cross-cut. Oblique impinging effects playing an important role inimprovement of heat transfer performance are acquired by the flow of arelatively high temperature around the fin wall and, thus, heat transferperformance is improved by 3.26% at most. In case 5 (C) having a moreincreased length of the cross-cut, it is judged that a flow rising fromthe bottom through the cross-cut causes impinging effects and heattransfer performance is more improved, as compared to case 4.

As results of pressure loss, as compared to the shape to which nocross-cut is applied, the case 2 (2/5 C) exhibits pressure loss which ismost highly increased by up to 6.16%. Since the central portion of aflow having large quantity of motion collides with the fin wall at therear of the cross-cut, such a result is expected. Next, case 3 exhibitspressure loss which is increased by up to 5.80%. Further, it isconfirmed that case 4, which causes the fewest flow disturbance,exhibits minimum pressure loss. A difference of heat transferperformance improvement degrees between case 2 and case 3 is only 0.05%but the pressure loss of case 3 is lower than that of case 2 by up to1%. Therefore, it may be understood that the optimal length of across-cut is 0.365 D_(h)(1/2 C) of case 3. Further, the interestingthing is that, in case 5 (c) at an Re 100, a heat transfer area isdecreased in proportion to increase of the length of the cross-cut andthus pressure loss becomes less than that of the case in which nocross-cut is applied.

As described above, as a result of research on the optimal length of across-cut, it is confirmed that heat transfer performance has maximumefficiency when the cross-cut has a size of 1/2 C=b/(2 sin(α)). If across-cut having the optimal length within the range of 100≦Re≦400 isapplied, heat transfer performance is increased by up to 22.9% andpressure loss is increased by up to 5.80%. Such heat transferperformance improvement is acquired by collision of the central portionof a flow having a relatively low temperature with the fin at the rearof the cross-cut due to flow disturbance formed by the cross-cut. On theother hand, it is confirmed that, if a cross-cut having a size of 4/5 Cis applied, heat transfer performance improvement is minimal.

Hereinafter, results of cross-cut analysis in accordance with embodiment2 and embodiment 3 will be analyzed from various points of view.

First, FIG. 14 illustrates partial Nu values when a wavy fin having nocut and the wavy fins of case 3 and case 4 are respectively divided into10 parts in the flow direction. As a result, it may be confirmed thatheat transfer at part 6, in which a cross-cut is applied to a positionat the rear of a peak, is greatly increased as in embodiment 2. Further,it may be confirmed that the Nu value of part 6 of case 3 having theoptimal length of a cross-cut in embodiment 3 is 3.02 times the Nu valueof the wavy fin having no cut and the Nu value of part 6 of case 4exhibiting the minimum performance improvement is 1.34 times the Nuvalue of the wavy fin having no cut. Further, it may be confirmed thatflow disturbance influence of the cross-cut is transmitted to a positionafter the cross-cut at the third wave and increases heat transferperformance of parts 7 to 10. However, it may be confirmed that, as aboundary layer is formed again, flow disturbance effects are reduced andheat transfer performance improvement at part 10 is not great.

FIG. 15 is a view illustrating a velocity streamline distribution and apressure contour line distribution under an Re of 400 in part 6 of case3 of embodiment 3. It may be confirmed that a recirculation section isformed just at the rear of the cross-cut and positive and negativepressure regions are formed due to oblique impinging. In general, if arecirculation section is formed, heat transfer performance of thecorresponding section is lowered. However, it is judged, as a result offlow disturbance in sections except for the corresponding section, heattransfer performance is greatly improved and offsets influence of therecirculation section.

Nest, j/f values of the wavy fin having no cut and the wavy fin of case3 of embodiment 3 within the range of 100≦Re≦400 are calculated andcompared, and FIG. 16 illustrates a result of comparison of thesevalues. Here, water is set as an operating fluid. Consequently, afterapplication of cross-cuts, a j/f value is increased by 3.02% at an Re of100, a j/f value is increased by 6.28% at an Re of 200, a j/f value isincreased by 7.91% at an Re of 300, and a j/f value is increased by8.60% at an Re of 400. This result may confirm that, if cross-cuts areapplied, improvement of heat transfer performance is greater thanincrease of pressure loss and the cross-cuts are effective in a wavyfin-type heat exchanger. Further, it may be confirmed that, as an Revalue increases, increase of j/f is high and, thus, as a flow becomesrapid, effects are increased.

Finally, in analysis of case 3 at an Re of 400, usefulness ε iscalculated and compared to a result of Nu analysis. Usefulness ε iscalculated by Equation 4 below and water is set as an operating fluid. Adifference between T_(w) and T_(in) is calculated as 10° C. in the samemanner as in validation. The usefulness equation refers to that given inHeat Transfer: A Practical Approach [23] of Yunus A. Cengel.

$\begin{matrix}{ɛ = \frac{Q_{w}}{\overset{.}{m}{c_{p}\left( {T_{w} - T_{in}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

FIG. 17 illustrates comparison results of usefulness ε and Nu. The Nuvalue of case 2 (2/5 C) and the Nu value of case 3 (1/2 C) are similar,with only a small difference of 0.05% therebetween, but the ε value ofcase 2 (2/5 C) is greater than the ε value of case 3 (1/2 C) by 0.38%.Further, as a cut length increases, a difference between ε and Nu valuesincreases. Such a difference is generated because the ε value means atotal heat transfer amount but the Nu value means a heat transfer amountper unit area, i.e., a heat flux. If the cross-cut technique is appliedto wavy fins, the cross-cut technique raises heat transfer performanceper unit area but reduces a heat transfer area. Since the heat transferperformances per unit area of case 2 and case 3 are not greatlydifferent but the heat transfer area of case 2 is greater than the heattransfer area of case 3, the total heat transfer amount of case 2 isgreater than the total heat transfer amount of case 3. It may beunderstood that, owing to the influence of the heat transfer area, as acut length increases, a difference between ε and Nu values increases.

As described above, if cross-cuts having the optimal length are appliedto the optimal position, a generated flow and heat transfercharacteristics are confirmed. As a result of calculation of partial Nuvalues in the flow direction, it is confirmed that heat transferperformance at the cross-cut application position is increased up to3.02 times, and influence of flow disturbance due to the cross-cut istransmitted to a position after the third wave and thus, heat transferperformance at the fin at the rear of the cut is also improved. In termsof characteristics of formation of a flow, if cross-cuts are applied, arecirculation section is generated at a position just at the rear of thecut and thus heat transfer performance of the corresponding section isrelatively low, but flow disturbance in sections except for thecorresponding section is active and thus heat transfer performance isimproved. Further, it may be confirmed through j/f values thatimprovement of heat transfer performance is greater than increase ofpressure and application of cross-cuts is effective. Finally, the totalheat transfer amount and heat transfer performance per unit area arecompared by comparing usefulness c and Nu values. As a result, it may beconfirmed that the optimal cut length is 2/5 C in terms of the totalheat transfer amount, and the optimal cut length is 1/2 C in terms ofheat transfer performance per unit area.

As apparent from the above description, the presently describedembodiments provide a wavy fin structure in which a cross-cut having adesignated length is formed at a designated position of a wavy fin andthus generates flow disturbance due to a wavy-type dynamic flow so as togreatly improve heat transfer performance.

Although the preferred embodiments have been disclosed for illustrativepurposes, those skilled in the art will appreciate that variousmodifications, additions and substitutions are possible, withoutdeparting from the scope and spirit of the disclosure as recited in theaccompanying claims.

What is claimed is:
 1. A wavy fin structure in which fins areperiodically arranged in a plurality of rows and each fin isperiodically waved to form repeated valleys and peaks in the lengthdirection of the fin, wherein a cross-cut having a designated length isformed around at least one valley or peak of the fin.
 2. The wavy finstructure according to claim 1, wherein the cross-cut is formed at avalley or a peak of the central portion of the fin in the lengthdirection of the fin.
 3. The wavy fin structure according to claim 2,wherein the cross-cut is formed at a position at the rear of the peak.4. The wavy fin structure according to claim 3, wherein the length ofthe cross-cut is${\frac{1}{5}C\mspace{14mu} {to}\mspace{14mu} \frac{4}{5}C},$wherein C is $\frac{b}{2\mspace{14mu} {\sin (\alpha)}},$ α is awarpage angle of the fin, and b is a fin pitch.
 5. The wavy finstructure according to claim 1, wherein a plurality of cross-cuts isformed at designated periods in the length direction of the fin.
 6. Thewavy fin structure according to claim 5, wherein the cross-cuts areformed at positions at the rear of peaks.
 7. The wavy fin structureaccording to claim 6, wherein the length of the cross-cuts is${\frac{1}{5}C\mspace{14mu} {to}\mspace{14mu} \frac{4}{5}C},$wherein C is $\frac{b}{2\mspace{14mu} {\sin (\alpha)}},$ α is awarpage angle of the fin, and b is a fin pitch.
 8. The wavy finstructure according to claim 1, wherein the wall of the fin connectingthe valleys and the peaks has a planar surface structure.
 9. A flat tubeheat exchanger having the wavy fin structure according to claim
 1. 10. Aflat tube heat exchanger having the wavy fin structure according toclaim 2.